MoeaBench v0.8.0 Technical Calibration Report

1. Methodology & Experimental Context

This report serves as the official scientific audit for MoeaBench v0.8.0. The objective is to validate and calibrate the numerical integrity and topological fidelity of the framework's core algorithms against established mathematical benchmarks (Ground Truth).

Experimental Setup

• Population Framework: All algorithms used a population size of N=200.
• Evolutionary Budget: Runs were executed for exactly 1000 generations.
• Statistical Baseline: Metrics in the summary tables are derived from 30 independent runs to ensure stochastical significance.
• Objective Space: All problems were configured with M=3 objectives for volumetric analysis.
• Normalization Strategy: We enforce Strict Theoretical Normalization. The [0, 1] range is mapped exclusively from the theoretical Ideal and Nadir points of the Ground Truth, not from observed data.

2. Metric Glossary & Interpretation

• IGD (Inverted Generational Distance): Measures both convergence (proximity) and diversity (spread). Lower is strictly better.
• EMD (Uniform): Earth Mover's Distance against a uniformized GT reference. Certification uses EMD_eff (ratio to calibrated floor for the same K), not a fixed absolute cutoff.
• Purity (GD_p95): 95th-percentile distance from population to GT. Certification uses Purity_eff (ratio to calibrated floor).
• H_raw: The absolute hypervolume calculated with Reference Point 1.1.
• H_ratio: $H_{raw} / RefBox$. Search area coverage (volume). Strictly $\le 1.0$.
• H_rel: $H_{raw} / H_{GT}$. Convergence to optimal front. Can exceed 100% due to saturation.
• T-conv (Stabilization): The generation where the algorithm reaches a stable state (within 5% of its final IGD value).
• Time (s): Average wall-clock execution time per run on the reference hardware.